Hello,
On Mon, Dec 09, 2002 at 05:36:23PM -0500, Raul Miller wrote:
> Analysis of quorum in the context of the election methods criteria
> documented at http://www.electionmethods.org/evaluation.htm:
>
> (1) Monotonicity criterion [Condorcet or Approval]
>
> The way I look at it, not submitting a ballot is a neutral act,
> favoring neither the default option nor any other option. Submitting
> a ballot is an act which may rank one over the other. Submitting a
> ballot ranking an option above the default option ranks that option
> higher. Submitting a ballot ranking an option below the default option
> ranks it lower.
>
> Quorum rule satisfies monotonicity because quorum is only satisfied
> by ballots which rank an option above the default option and quorum
> will never be caused to not be satisfied by any such ballot once
> it has been satisfied.
>
> Criterion which are only satisfied by Condorcet:
> (2) Condorcet Criterion
> (3) Generalized Condorcet Criterion
>
> Quorum rule does not satisfy these criterion.
>
> For example: quorum is 45, A and B require 1:1 majority, D is the default
> option, three votes are received: 2 ABD, 1 BAD. The election defaults.
>
> (4) Strategy Free Criterion [Condorcet only]
> (5) Generalized Strategy-Free Criterion [Condorcet only]
> (6) Strong Defensive Strategy Criterion [Condorcet only]
> (7) Weak Defensive Strategy Criterion [Condorcet or Approval]
>
> If we classify "the election defaults" as "not a candidate", quorum
> would satisfy these criterion.
>
> If we classify "the election defaults" as "a candidate" then quorum
> does not satisfy any of these criterion [the three vote
> example, above, illustrates this failure for all criterion].
>
> (8) Favorite Betrayal Criterion [Approval only]
>
> The quorum portion of the rules satisfies this criterion, the proof is
> essentially the same as for monotonicity. However, since the underlying
> system does not satisfy this criterion the point is moot.
>
> (9) Summability Criterion [Condorcet and Approval]
>
> Quorum satisfies this criterion. Proof: we can add an additional row
> and column to the tally table to represent quorum, and another set of
> rows and columns to label which option is the default option, and have
> each vote add 0 to the these, now all information needed to determine
> the outcome of the vote is in this summable array.
So this is price. The obvious question is:
what does it buy us? Is it worth the price?
What do you think?
Jochen
--
Omm
(0)-(0)
http://www.mathematik.uni-kl.de/~wwwstoch/voss/index.html
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